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SUMMARY:Resonances as a computational tool
DTSTART:20240119T141500
DTEND:20240119T153000
DTSTAMP:20260407T144154Z
UID:ede30c5f68987375ce84f6af44431e1b69bc70982758e476288b2aaf
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Katharina Schratz\, Sorbonne University\, Laboratoire Ja
 cques-Louis Lions - Paris\n \nA large toolbox of numerical schemes for di
 spersive equations has been established\, based on different discretizatio
 n techniques such as discretizing the variation-of-constants formula (e.g.
 \, exponential integrators) or splitting the full equation into a series o
 f simpler subproblems (e.g.\, splitting methods). In many situations these
  classical schemes allow a precise and efficient approximation. This\, how
 ever\, drastically changes whenever non-smooth phenomena enter the scene s
 uch as for problems at low regularity and high oscillations. Classical sch
 emes fail to capture the oscillatory nature of the solution\, and this may
  lead to severe instabilities and loss of convergence. In this talk I pres
 ent a new class of resonance based schemes. The key idea in the constructi
 on of the new schemes is to tackle and deeply embed the underlying nonline
 ar  structure of resonances into the numerical discretization. As in the 
 continuous case\, these terms are central to structure preservation and of
 fer the new schemes strong geometric properties at low regularity.
LOCATION:MA A1 10 https://plan.epfl.ch/?room==MA%20A1%2010
STATUS:CONFIRMED
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